Experiments with nonlinear extensions to SCIP

Abstract This paper describes several experiments to explore the options for solving a class of mixed integer nonlinear programming,problems that stem from a real-world mine production planning project. The only type of nonlinear constraints in these problems are bilinear equalities involving continuous variables, which enforce the ratios between ele- ments in mixed material streams. A branch-and-bound algorithm to handle the integer variables has been tried in another project. However, this branch-and-bound algo- rithm is not effective for handling the nonlinear constraints. There- fore state-of-the-art nonlinear solvers are utilized to solve the resulting nonlinear subproblems in this work. The experiments were carried out using the NEOS server for optimization. After finding that current nonlinear programming,solvers seem to lack suitable preprocessing ca- pabilities, we preprocess the instances beforehand and use a heuristic approach to solve the nonlinear subproblems. In the appendix, we explain how to add a polynomial constraint handler that uses IPOPT as embedded,nonlinear programming,solver for the constraint programming,framework SCIP. This is one of the crucial steps for implementing our algorithm in SCIP. We briefly de-